Kernel-based learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information is contained in the so-called kernel matrix, a symmetric and positive definite matrix that encodes the relative positions of all points. Specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input space---classical model selection problems in machine learning. In this paper we show how the kernel matrix can be learned from data via semi-definite programming (SDP) techniques. When applied

Kernel methods in general and support vector machines in particular have been successful in various learning tasks on data represented in a single table. Much 'real-world ' data, however, is structured- it has no natural representation in a single table. Usually, to apply kernel methods to 'realworld' data, extensive pre-processing is performed toembed the data into areal vector space and thus in a single table. This survey describes several approaches ofdefining positive definite kernels on structured instances directly.

We investigate the problem of learning optimal descriptors for a given classification task. Many hand-crafted descriptors have been proposed in the literature for measuring visual similarity. Looking past initial differences, what really distinguishes one descriptor from another is the tradeoff that it achieves between discriminative power and invariance. Since this trade-off must vary from task to task, no single descriptor can be optimal in all situations. Our focus, in this paper, is on learning the optimal tradeoff for classification given a particular training set and prior constraints. The problem is posed in the kernel learning framework. We learn the optimal, domain-specific kernel as a combination of base kernels corresponding to base features which achieve different levels of trade-off (such as no invariance, rotation invariance, scale invariance, affine invariance, etc.) This leads to a convex optimisation problem with a unique global optimum which can be solved for efficiently. The method is shown to achieve state-of-the-art performance on the UIUC textures, Oxford flowers and Caltech 101 datasets. 1.

This paper addresses the problem of choosing a kernel suitable for estimation with a Support Vector Machine, hence further automating machine learning. This goal is achieved by defining a Reproducing Kernel Hilbert Space on the space of kernels itself. Such a formulation leads to a statistical estimation problem very much akin to the problem of minimizing a regularized risk functional.

We study the problem of finding an optimal kernel from a prescribed convex set of kernels K for learning a real-valued function by regularization. We establish for a wide variety of regularization functionals that this leads to a convex optimization problem and, for square loss regularization, we characterize the solution of this problem. We show that, although K may be an uncountable set, the optimal kernel is always obtained as a convex combination of at most m+2 basic kernels, where m is the number of data examples. In particular, our results apply to learning the optimal radial kernel or the optimal dot product kernel. 1.

Abstract. Support Vector Machines (SVM) have been extensively studied and have shown remarkable success in many applications. However the success of SVM is very limited when it is applied to the problem of learning from imbalanced datasets in which negative instances heavily outnumber the positive instances (e.g. in gene profiling and detecting credit card fraud). This paper discusses the factors behind this failure and explains why the common strategy of undersampling the training data may not be the best choice for SVM. We then propose an algorithm for overcoming these problems which is based on a variant of the SMOTE algorithm by Chawla et al, combined with Veropoulos et al’s different error costs algorithm. We compare the performance of our algorithm against these two algorithms, along with undersampling and regular SVM and show that our algorithm outperforms all of them. 1

The standard representation of text documents as bags of words suffers from well known limitations, mostly due to its inability to exploit semantic similarity between terms. Attempts to incorporate some notion of term similarity include latent semantic indexing [8], the use of semantic networks [9], and probabilistic methods [5]. In this paper we propose two methods for inferring such similarity from a corpus. The first one defines word-similarity based on document-similarity and viceversa, giving rise to a system of equations whose equilibrium point we use to obtain a semantic similarity measure. The second method models semantic relations by means of a diffusion process on a graph defined by lexicon and co-occurrence information. Both approaches produce valid kernel functions parametrised by a real number. The paper shows how the alignment measure can be used to successfully perform model selection over this parameter. Combined with the use of support vector machines we obtain positive results.

In biological data, it is often the case that observed data are available only for a subset of samples. When a kernel matrix is derived from such data, we have to leave the entries for unavailable samples as missing. In this paper, the missing entries are completed by exploiting an auxiliary kernel matrix derived from another information source. The parametric model of kernel matrices is created as a set of spectral variants of the auxiliary kernel matrix, and the missing entries are estimated by fitting this model to the existing entries. For model fitting, we adopt the em algorithm (distinguished from the EM algorithm of Dempster et al., 1977) based on the information geometry of positive definite matrices. We will report promising results on bacteria clustering experiments using two marker sequences: 16S and gyrB.

We describe several families of k-mer based string kernels related to the recently presented mismatch kernel and designed for use with support vector machines (SVMs) for classification of protein sequence data. These new kernels – restricted gappy kernels, substitution kernels, and wildcard kernels – are based on feature spaces indexed by k-length subsequences (“k-mers”) from the string alphabet Σ. However, for all kernels we define here, the kernel value K(x,y) can be computed in O(cK(|x|+|y|)) time, where the constant cK depends on the parameters of the kernel but is independent of the size |Σ | of the alphabet. Thus the computation of these kernels is linear in the length of the sequences, like the mismatch kernel, but we improve upon the parameter-dependent constant cK = k m+1 |Σ | m of the (k,m)-mismatch kernel. We compute the kernels efficiently using a trie data structure and relate our new kernels to the recently described transducer formalism. In protein classification experiments on two benchmark SCOP data sets, we show that our new faster kernels achieve SVM classification performance comparable to the mismatch kernel and the Fisher kernel derived from profile hidden Markov models, and we investigate the dependence of the kernels on parameter choice.

We show that the Gaussian random fields and harmonic energy minimizing function framework for semi-supervised learning can be viewed in terms of Gaussian processes, with covariance matrices derived from the graph Laplacian. We derive hyperparameter learning with evidence maximization, and give an empirical study of various ways to parameterize the graph weights.